I'd do some heard research before asking a lot of those questions. NALP answers almost all your questions about billables, and some firms may include some of those answers on their websites (especially if this is a summer program re: how work is assigned, etc.).
Typically, if it's a callback sort of situation, I usually ask "personal" questions about the interviewer's experiences in the firm, why they like it there or chose this firm, what kind of training opportunities they've had, etc. If I'm interviewing with a partner or senior associate who has been with the firm for a good number of years, I occasionally asked about how the firm's grown in the last 5 years, how that person's practice has evolved (esp if it's a practice area I'm interested in), and where the person thinks the firm may be heading in terms of growth strategy.
My ultimate goal with questions was to *never* ask a question that is clearly answered somewhere easily accessible, to tap into the interviewer's personal experiences/opinions (which also shows that you are interested in the person you're speaking to, something that everyone typically appreciates), and to try to get a sense of what the firm is like and where the firm is going.